A popular pastime is to see who can push an object closest to the edge of a table without its going off. You push the 100 g object and release it 2.90 from the table edge. Unfortunately, you push a little too hard. The object slides across, sails off the edge, falls 1.50 to the floor, and lands 35.0 from the edge of the table. If the coeffecient of friction is .3 what is the objects speed as you released it?
I found the velocity in the x direction when the object falls off the table to be .63 m/s. how do i find the initial velocity?
Since you mentioned 0.63 m/s, but the mass of the object is 100 g, there is uncertainty as to what unit is being used. You may want to include units in your future questions.
There are two stages of the motion of the object.
Stage 1: movement on the table, and
stage 2: free fall with horizontal velocity.
I will tackle stage 2 first, since all data are given.
First, consider vertical movement.
v0=0 m/s
a=-9.8 m/s²
Vertical distance,
Sv = v0*t + (1/2)at² = -1.5
Solving for t
t=sqrt(2Sv/a)
During this time, the object has travelled Sh metres.
Thus horizontal velocity, Vh
= Sh/t
For the stage 1 motions,
v0 = initial velocity, to be found
vh = final velocity, found above
acceleration = -μg due to friction
Distance, S=2.9 m
Use
vh²-v0²=2aS to solve for v0.
How much momentum is acquired by a 75 kg sky-diver in free fall in 2.0 minutes after jumping from the plane?
To find the initial velocity of the object as you released it, you can use the concept of conservation of energy. Since there is no air resistance and the only force acting on the object is friction, the total mechanical energy of the object is conserved.
The total mechanical energy of the object can be calculated as the sum of its potential energy and kinetic energy. At the edge of the table, all of the object's energy is in the form of potential energy, given by:
PE = m * g * h
Where:
m = mass of the object = 0.100 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height above the ground = 2.90 m
PE = 0.100 kg * 9.8 m/s^2 * 2.90 m
PE = 2.834 J
When the object falls off the table and reaches the floor, all of its initial potential energy is converted into kinetic energy:
KE = 1/2 * m * v^2
Where:
v = velocity of the object as you released it (to be determined)
Since the object slides off the table, there is work done by the friction force:
Work_done_by_friction = force_friction * d
Where:
force_friction = coefficient_of_friction * normal_force
d = distance from the edge of the table to where the object lands = 35.0 m
The normal force is equal in magnitude and opposite in direction to the force of gravity, so the work done by friction is:
Work_done_by_friction = coefficient_of_friction * m * g * d
Setting the work done by friction equal to the change in potential energy, we have:
coefficient_of_friction * m * g * d = PE
Substituting the given values:
0.3 * 0.100 kg * 9.8 m/s^2 * 35.0 m = 2.834 J
Simplifying:
1.029 J = 2.834 J
This indicates that there is an error in the given information or calculations. Please double-check your calculation or provide additional information to proceed.
To find the initial velocity of the object before it fell off the table, we need to consider conservation of energy.
The initial potential energy of the object, when it is released from a distance of 2.9 m from the table edge, can be calculated as:
PE_initial = m * g * h
where m is the mass of the object (100 g or 0.1 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height from the table edge to the floor (1.50 m).
PE_initial = 0.1 kg * 9.8 m/s^2 * 1.50 m
PE_initial = 1.47 J
At the edge of the table, the object has both potential energy and kinetic energy.
The potential energy at that point, considering the height of the table, can be calculated as:
PE_table = m * g * h_table
where h_table is the height from the table edge to the floor (1.50 m).
PE_table = 0.1 kg * 9.8 m/s^2 * 1.50 m
PE_table = 1.47 J
The kinetic energy at that point can be calculated as:
KE_table = 0.5 * m * v_table^2
where v_table is the velocity of the object at the edge of the table (which we are trying to find).
KE_table = 0.5 * 0.1 kg * v_table^2
Now, considering friction, the work done by friction can be calculated as:
Work_friction = m * g * μ * x
where μ is the coefficient of friction (0.3 in this case) and x is the horizontal distance traveled by the object after falling off the table (35.0 m).
Work_friction = 0.1 kg * 9.8 m/s^2 * 0.3 * 35.0 m
Work_friction = 10.29 J
Since energy is conserved, the initial potential energy of the object is equal to the sum of its kinetic energy at the edge of the table and the work done by friction:
PE_initial = KE_table + Work_friction
1.47 J = 0.5 * 0.1 kg * v_table^2 + 10.29 J
Rearranging the equation to solve for v_table:
0.5 * 0.1 kg * v_table^2 = 1.47 J - 10.29 J
0.5 * 0.1 kg * v_table^2 = -8.82 J
Since the result is negative, we know there is not enough initial velocity for the object to reach the edge of the table, so there may be a calculation error or missing information. Please double-check the given values and equations to ensure accuracy.